- Lie derivative
- Exterior product
- Tensor product
- Hodge operator
- Covariant derivative
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Connection with torsion
This notebook illustrates how to use the Atlas package to make calculations with user defined connections.
Examples:
| Functions[f1→f1[x1,x2,...,xn],f2→f2[y1,y2,...,ym],..., fk→fk[z1,z2,...,zj]] | fk→fk(z1, z2, ..., zj) - equations where fk-function identifier and zj - variables. |
| Vectors[v1,v2,...,vi,...,vn] | vi - vector identivier. |
| Forms[f1→n,f2→k,...,fi→p] | fi→p - equations where fi - form identifier and p is a variable or an integer - the form's degree. |
| Coframe[id1→ expr1,id2→ expr2,...idn→ exprn] | id - identifier for indexed variable - the coframe 1-forms n - dimension of working manifold (a variable or integer) idi → expri - equation where idi is indexed variable - coframe 1-form and expri is decomposition of the 1-form on exact 1-forms. |
| Frame[idj] | idj -indexed variable the frame vectors |
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| Connection[id] | id - variable - connection identifier. |
| Curvature[id | id-variable-curvature identifier. |
| Torsion[id] | id - variable - torsion identifier. |
| Riemann[id] | id - variable - corresponding identifier. |
| Ricci[id] | id - variable - corresponding identifier. |
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